In conventional fan beam transmission tomography, such as utilized in x-ray computed tomography (x-ray CT), the attenuation of a fan beam of x-rays is measured as this beam probes medium along many different trajectories. The information contained in these attenuation projections is then used to reconstruct a tomographic image of the medium. The success of x-ray CT (manifested in the resolution and clarity of the images) is fundamentally linked to the very short wavelength of the incident x-ray beam (.apprxeq.1 .ANG.). The mathematical reconstruction techniques assume a geometrical ray approximation and are quite simplified.
In ultrasonic tomography, the acoustic wavelengths (.apprxeq.1 mm) are on the order of the scale size of the inhomogeneities of the medium and the diffraction effects of the acoustic wave are not negligible. In this case, the attenuation of a sound wave is substantially affected by scattering effects such as diffraction, refraction, and reflection, as well as absorption. The simplified mathematical reconstruction algorithms used in conventional x-ray CT are not applicable in this case.
Ultrasonic diffraction tomography (UDT) techniques attempt to mathematically reconstruct a tomographic image of a medium from acoustic wave data with full consideration to the scattering effects associated with acoustic wavelengths involved. This is done by considering the full wave equation, a much more difficult problem to develop and implement than the geometrical wave approximation reconstruction methods used in x-ray CT. UDT techniques attempt to determine the internal structure of an object which is semi-transparent to acoustic waves from a set of scattered wave data detected outside at the boundary of the object. A number of these mathematical techniques have been theoretically considered, including simplified algorithms which use the Born approximation (E. Wolf, "Three-dimensional Structure Determination of Semi-Transparent Objects from Holographic Data", Opt. Comm. 153-156 (1969)) and Rytov approximations (A. J. Devaney, "Inverse Scattering Within the Rytov Approximation", Opt. Lett. 6, 374 (1981)). The Born and Rytov approximations assume that the medium which is imaged is a weak scatterer of acoustic waves and that the acoustic wave does not experience large phase shifts within the medium. Computer intensive full-wave reconstruction algorithms (S. Johnson and M. Tracy, "Inverse Scattering Solutions By a Sinc Basis, Multiple Source, Moment Method", Ultrasonic Imaging 5, 361-375 (1983) and references therein) have also been proposed for imaging mediums under conditions which are not in the range of validity of the Born or Rytov approximation.
Prior art patents included Devaney (U.S. Pat. Nos. 4,598,366 and 4,594,662) and Johnson (U.S. Patent No. 4,662,222). The patents of Johnson disclose iterative algorithms which form an initial estimate of the sound speed at all points within the object being imaged, calculate a sound speed map (a type of image), and then update the map. This process is repeated until a residual error parameter is small enough. The patents of Devaney form an image directly from the data using Born and Rytov inversions with a technique called filtered back propagation.